Characterization of hyperfine interaction between an NV electron spin and a first-shellC13nuclear spin in diamond

Abstract

The Nitrogen-Vacancy (NV) center in diamond has attractive properties for a number of quantum technologies that rely on the spin angular momentum of the electron and the nuclei adjacent to the center. The nucleus with the strongest interaction is the 13 C nuclear spin of the first shell. Using this degree of freedom effectively hinges on precise data on the hyperfine interaction between the electronic and the nuclear spin. Here, we present detailed experimental data on this interaction, together with an analysis that yields all parameters of the hyperfine tensor, as well as its orientation with respect to the atomic structure of the center.PACS numbers: 03.67. Lx, 76.70.Hb, 33.35.+r, 61.72.JNitrogen-Vacancy (NV) centers in diamond have interesting properties for applications in room-temperature metrology, spectroscopy, and Quantum Information Processing (QIP) [1][2][3][4][5][6]. Nuclear spins, coupled by hyperfine interaction to the electron spin of the NV-center, are important for many of these applications [1,3,[6][7][8][9][10][11][12][13]. For example, in QIP applications, the nuclear spins can hold quantum information [12,13], serving as part of a quantum register [1]. Accurate knowledge of the hyperfine interaction is necessary, e.g., for designing precise and fast control sequences for the nuclear spins [14,15]. With a known Hamiltonian, control sequences can be tailored by optimal control techniques to dramatically improve the speed and precision of multi-qubit gates [16][17][18][19].The 13 C nuclear spin of the first coordination shell is a good choice for a qubit due to its large hyperfine coupling to the electronic spin of the NV center, which can be used to implement fast gate operations [3,20,21] or highspeed quantum memories [22]. Full exploitation of this potential requires accurate knowledge of the hyperfine interaction, including the anisotropic (tensor) components. The interaction tensor has been calculated by , but only a limited number of experimental studies of this hyperfine interaction exist to date [27][28][29]. In this work, we present a detailed analysis of this hyperfine interaction. The experiments were carried out on single NV centers of a diamond crystal with a natural abundance of 13 C and a nitrogen concentration of < 5 ppb using a home-built confocal microscope and microwave electronics for excitation [22].The presence of a nuclear spin in the first coordination shell reduces the symmetry of the NV center from C 3V to C S , a single mirror plane. This symmetry plane passes through the NV symmetry axis and the 13 C nuclear spin as illustrated in Fig. 1(a). The NV symmetry axis defines the z-axis of the NV frame of reference, the x-axis lies in the symmetry plane of the center, and the y-axis is perpendicular to both of them. Due to the symmetry of the system, only those elements of the hyperfine tensor that are invariant with respect to the inversion of the y-coordinate can be non-zero. Hence, the hyperfine Hamiltonian in the NV frame of reference can be written as(1) Here, S α an...

Non-flipping13C spins near an NV center in diamond: hyperfine and spatial characteristics by density functional theory simulation of the C510[NV]H252cluster

“…From equation (5) it follows that the dipolar terms vanish if the spin density r +   ( ) r R S n observed from the point of the 13 C nucleus is highly symmetric. As pointed out previously [23], an arbitrary NV− 13 C spin system possesses symmetry C S , which means that in the specific NV-PACS having XZ plane passing through this definite 13 C nucleus and containing the NV axis, the spin density will be symmetric with respect to the change Y to -Y, resulting in the zeroing out of the matrix element T ZY in (5). We verified numerically that in the transformed hfi matrices ¢ A KL for each position of 13 C in our cluster the element T ZY (and, additionally, elements T XY =T YX , T YZ =T ZY ) was zero.…”

“…In the general case the matrix A KL of the tensor (2a) is non-diagonal in the NV-PACS due to the presence of non-diagonal elements in the dipole−dipole term T KL at K ≠ L. However, symmetry properties allow the zeroing out of some of them. In particular, for each NV− 13 C spin system the T KL matrix can be simplified by choosing the X axis in such a way that the XZ plane passes through the 13 C atom of the system [23]. In this specific NV− 13 C-PACS, all elements of the respective hfi matrix ¢ A KL being non-invariant with respect to the inversion of the Y coordinate are zero due to the C S symmetry of the system.…”

“…In this specific NV− 13 C-PACS, all elements of the respective hfi matrix ¢ A KL being non-invariant with respect to the inversion of the Y coordinate are zero due to the C S symmetry of the system. The hfi term then takes the form [23]:…”

Optical Detection of Magnetic Resonance

“…splitting into a doublet (of the triplet due to the 14 N interaction), it results here into a quartet (Rao and Suter, 2016). This is a consequence of the different orientations of the nuclear spin quantisation axes in the different electron spin states.…”

Repetitive readout enhanced by machine learning

“…Correspondingly, the dark state is | = + ñ m 1 I , and bright state is | = -ñ m 0, 1 I . We remark that it is possible to use the same protocol to read out 13 C rather than 14 N [13-16], given wellcharacterized hyperfine interaction strengths [46][47][48][49].…”